Oleh J. Tretiak

Multidimensional alignment using the Euclidean distance transform

Abstract We present a methodology for alignment of multidimensional data sets that is based on the Euclidean distance transform and the Marquardt–Levenberg optimization algorithm. The proposed approach operates on pixel or voxel descriptions of objects to be matched and estimates the parameters of a space transformation for optimal alignment of objects. The computational cost of an algorithm developed with this method is estimated. The methodology is tested by developing an algorithm for rigid body transformation alignment of three-dimensional data sets. Tests with synthetic and real objects indicate that the method is accurate, reliable, and robust.

Informatics center for mouse genomics: the dissection of complex traits of the nervous system.

In recent years, there has been an explosion in the number of tools and techniques available to researchers interested in exploring the genetic basis of all aspects of central nervous system (CNS) development and function. Here, we exploit a powerful new reductionist approach to explore the genetic basis of the very significant structural and molecular differences between the brains of different strains of mice, called either complex trait or quantitative trait loci (QTL) analysis. Our specific focus has been to provide universal access over the web to tools for the genetic dissection of complex traits of the CNS—tools that allow researchers to map genes that modulate phenotypes at a variety of levels ranging from the molecular all the way to the anatomy of the entire brain.Our website, The Mouse Brain Library (MBL; http://mbl.org) is comprised of four interrelated components that are designed to support this goal: The Brain Library, iScope, Neurocartographer, and WebQTL. The centerpiece of the MBL is an image database of histologically prepared museum-quality slides representing nearly 2000 mice from over 120 strains—a library suitable for stereologic analysis of regional volume. The iScope provides fast access to the entire slide collection using streaming video technology, enabling neuroscientists to acquire high-magnification images of any CNS region for any of the mice in the MBL. Neurocartographer provides automatic segmentation of images from the MBL by warping precisely delineated boundaries from a 3D atlas of the mouse brain. Finally, WebQTL provides statistical and graphical analysis of linkage between phenotypes and genotypes.

Elastic 3-D alignment of rat brain histological images

A three-dimensional wavelet-based algorithm for nonlinear registration of an elastic body model of the brain is developed. Surfaces of external and internal anatomic brain structures are used to guide alignment. The deformation field is represented with a multiresolution wavelet expansion and is modeled by the partial differential equations of linear elasticity. A progressive estimation of the registration parameters and the usage of an adaptive distance map reduce algorithm complexity, thereby providing computational flexibility that allows mapping of large, high resolution datasets. The performance of the algorithm was evaluated on rat brains. The wavelet-based registration method yielded a twofold improvement over affine registration.

Design and implementation of software for assembly and browsing of 3D brain atlases

Visualization software for three dimensional digital brain atlases present many challenges in design and implementation. These challenges include the design of an effective human interface, management of large data sets, display speed when slicing the data set for viewing/browsing, and the display of delineated volumes of interest (VOI). We present a software design, implementation and storage architecture that addresses these issues, allowing the user to navigate through a reconstructed volume quickly and smoothly, with an easy-to-use human interface. The software (macostat, for use with Macintosh OS) allows the user to rapidly display slices of the digital atlas at any arbitrary slicing angle, complete with delineated VOIs. The VOIs can be assigned colors of the users choosing. The entire atlas, or selected portions, may be resliced with slices stored as individual image files, complete with delineations. These delineations may be transferred to corresponding sections of experimental materials using our analysis program (brain). The software may be obtained from the laboratorys web site: http://www.neuroterrain.org

Regular ArticleThree-Dimensional Reconstruction of Activated Columns from 2-[14C]Deoxy-d-glucose Data

Three-dimensional (3-D) reconstruction of autoradiograms can provide new insights into the functional relationship of neural regions. To reach full potential, however, 3-D reconstruction must be both accurate and efficient. In this paper, we present a novel image matching algorithm that simultaneously aligns a set of serial sections and uses the method to reconstruct whisker barrels from the rat cerebral cortex. We initially compared several alignment techniques and found that our Multi-Set Registration (MSR) algorithm produced superior accuracy. This algorithm is based on a least-squares minimization technique and is able to simultaneously register a set of serial sections with subpixel precision (30-micron accuracy). We applied our new technique to the 3-D reconstruction of a series of autoradiograms. Our objective was to visualize and measure the 3-D metabolic (functional) shape of normal (control) and developmentally altered (plastic) C3 vibrissa columns in the first somatosensory area of the rat cerebral cortex. The plastic C3 metabolic column showed a nearly 450% increase in volume when compared to the control column. In addition, the lesion-altered C3 column-in contrast to the normal C3 column-displayed no central zone of high activity, and patches of higher metabolic activity were scattered throughout the columnar profile. This metabolic activity was not confined to the cylindrical column, but extended tangentially as radiating fingerlike projections toward neighboring barrels.

Surface-based matching using elastic transformations

Abstract We introduce a methodology for the alignment of multidimensional data, such as brain scans. The proposed approach does not require fiducial-point correspondence; correspondence of surfaces provides sufficient data for registration. We extend multidimensional interpolation theory by using a more general form of energy functional, which leads to basis functions that have different orders at zero and infinity. This allows flexibility in the design of the interpolation solution. The problem is transformed into a linear algebra problem. Two techniques for better conditioning of the system matrix are described. Experimental results on two- and three-dimensional alignment of brain data used in neurochemistry research are shown.

Surface alignment of an elastic body using a multiresolution wavelet representation

An algorithm for nonlinear registration of an elastic body is developed. Surfaces (outlines) of known anatomic structures are used to align all other (internal) points. The deformation field is represented with a multiresolution wavelet expansion and is modeled by the partial differential equations of linear elasticity. A hierarchical approach that reduces algorithm complexity is adopted. The performance of the algorithm is evaluated by two-dimensional alignment of sections from mouse brains located in the olfactory bulbs. The registration algorithm was guided by manually delineated contours of a subset of brain structures and validated based on another subset of brain structures. The wavelet alignment algorithm produced a twofold to fivefold improvement in accuracy over an affine (linear) alignment algorithm.

Numerical solution of the direct scattering problem through the transformed acoustical wave equation.

A transformation is applied to the acoustical wave equation to obtain a new equivalent form that does not contain gradients of the pressure. A new technique, based on the spectral method, is developed for the numerical solution of the direct time domain scattering problem. Modeling techniques for obtaining accurate solutions are discussed and numerical examples are presented.

The analytic and functional accuracy of a video densitometry system

Applications using radiotracers and quantitative film autoradiography are increasing dramatically in the neurosciences. Microcomputer-based image analyzing systems with video input have been developed to provide rapid quantification of autoradiographic images on relatively inexpensive systems. However, there has been some question as to whether such systems can reliably produce high levels of densitometric accuracy, especially when compared to mechanical scanners which are standard in research requiring extreme fidelity of measurement. We report methods and results from tests done to determine the analytical and functional accuracy of the Drexel Unix-based Microcomputer image Analysis System (DUMAS), which is a video densitometric system designed to provide quantitative data from autoradiograms. Analytical accuracy was determined by measuring photometric uniformity, the optical density transfer function, temporal stability, geometric uniformity, and flare. In addition, data are provided on the resolution of the system at several magnifications. Functional accuracy, the accuracy of the estimates of mean isotope concentrations in diverse neural structures, was determined by comparing the results obtained on the DUMAS system with the results from analyzing the same [14C]2-deoxyglucose images with two different Optronics P1000 systems. Our results show that, provided care is taken in the choice of a camera and a light source, the analytic accuracy of videodensitometry is high. Its functional accuracy is also high in that measurements of radioisotope concentrations in diverse neural structures made on the DUMAS system agree closely with the measurements from a properly adjusted Optronics P1000 system. The rapidity and economy of videodensitometry is not, therefore, obtained at the sacrifice of densitometric accuracy. Given adequately tested hardware and provided that suitable checks on instrument calibration and adjustment are made, the errors in autoradiographic quantification due to the image analyzing system itself are minor in comparison to other sources of error, including, as we show, variations in the users delineation of the boundaries of neural structures.

Ultrasound imaging through time-domain diffraction tomography

Time-domain diffraction tomography, a technique for imaging with acoustic (and other) fields in which a medium parameter, such as density, can be mapped from scatter data collected from one pulse, is discussed. When Born approximations hold, the technique provides an exact inversion of the acoustical scattering equations. Computer simulation of the time-domain diffraction tomography equations indicates that under ideal conditions, and when the Born approximation is valid, the method can reconstruct maps of parameter variations. However, when data are collected from an incident pulse whose bandwidth is limited, the reconstruction is no longer perfect. A simple question is derived that characterizes the performance of time-domain diffraction tomography, and the limitations are explained as the effect of a spatial filter that eliminates some of the spatial frequencies. Relations between the object parameters, pulse bandwidth, and reconstruction accuracy are investigated with numerical experiments.<<ETX>>